3 papers
math.CO2026
Albertson's Conjecture Holds for r at Most 26
Ankan Sadhu
Albertson conjectured that every graph with chromatic number r has crossing number at least cr(K_r). The conjecture was verified for r <= 12 by Albertson, Cranston and Fox, for r <…
math.CO2026
An improved upper bound for the Zarankiewicz number z(43;2) <= 294 via structural rigidity, including hexary packing number pa(5;6) = 31
Ankan Sadhu
The Zarankiewicz number z(n;2) is the largest number of ones in an n x n zero-one matrix with no all-one 2x2 submatrix. At n=43, the Kovari-Sos-Turan bound, sharpened by Reiman, gi…
math.CO2026
A congruence obstruction to Roman's bound for Zarankiewicz numbers
Ankan Sadhu
Let z(m,n;s,t) be the largest number of ones in an m x n zero-one matrix with no s x t all-ones submatrix. Roman's 1975 inequality remains the best general upper bound for s>=3, bu…